mlsanityData to 14 Oct 2026

Soft Diffusion: Score Matching for General Corruptions

arXiv 2209.05442 ↗First posted 12 Sep 2022cs.CV cs.AI cs.LGcited by 102

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We define a broader family of corruption processes that generalizes previously known diffusion models. To reverse these general diffusions, we propose a new objective called Soft Score Matching that provably learns the score function for any linear corruption process and yields state of the art results for CelebA. Soft Score Matching incorporates the degradation process in the network. Our new loss trains the model to predict a clean image, textitthat after corruption, matches the diffused observation. We show that our objective learns the gradient of the likelihood under suitable regularity conditions for a family of corruption processes. We further develop a principled way to select the corruption levels for general diffusion processes and a novel sampling method that we call Momentum Sampler. We show experimentally that our framework works for general linear corruption processes, such as Gaussian blur and masking. We achieve state-of-the-art FID score 1.85 on CelebA-64, outperforming all previous linear diffusion models. We also show significant computational benefits compared to vanilla denoising diffusion.

Key facts. Cited by 102 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 47 of its 57 references that are in the map. First posted on arXiv 12 Sep 2022.

Builds on

47 of 57 references.

Closest ancestors · 23

Same direction, newest first

  1. 2022Diffusion Models in Vision: A Survey10 Sep
  2. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  3. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise19 Aug
  4. 2022Pyramidal Denoising Diffusion Probabilistic Models3 Aug
  5. 2022Progressive Deblurring of Diffusion Models for Coarse-to-Fine Image Synthesis16 Jul
  6. 2022Accelerating Score-based Generative Models for High-Resolution Image Synthesis8 Jun
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  8. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  9. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  10. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  11. 2021Heavy-tailed denoising score matching17 Dec
  12. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
11 more
  1. 2021Denoising Diffusion Gamma Models10 Oct
  2. 2021Variational Diffusion Models1 Jul
  3. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation10 Jun
  4. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
  5. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  6. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  7. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  8. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  9. 2020Denoising Diffusion Implicit Models6 Oct
  10. 2020Denoising Diffusion Probabilistic Models19 Jun
  11. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 24

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  3. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2018Neural Ordinary Differential Equationscited by 3,779
  6. 2022Video Diffusion Modelscited by 2,305
  7. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  8. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  9. 2022Denoising Diffusion Restoration Modelscited by 963
  10. 2021Blended Diffusion for Text-driven Editing of Natural Imagescited by 927
  11. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 677
  12. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 508
12 more
  1. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 286
  2. 2021Deblurring via Stochastic Refinementcited by 249
  3. 2021Autoregressive Diffusion Modelscited by 210
  4. 2022Speech Enhancement and Dereverberation with Diffusion-based Generative Modelscited by 197
  5. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  6. 2022Generative Modelling With Inverse Heat Dissipationcited by 167
  7. 2022Optimal Transport Tools (OTT): A JAX Toolbox for all things Wassersteincited by 101
  8. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 97
  9. 2020Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimationcited by 88
  10. 2022Universal Speech Enhancement with Score-based Diffusioncited by 75
  11. 2021Beyond In-Place Corruption: Insertion and Deletion In Denoising Probabilistic Modelscited by 23
  12. 2022Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problemscited by 11

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 11; 2023: 44; 2024: 19; 2025: 16; 2026: 12.

102 papers.

Sort:

By area:

  1. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 395
  2. 2022DiffRF: Rendering-Guided 3D Radiance Field Diffusioncited by 204
  3. 2024A Survey on Diffusion Models for Inverse Problemscited by 180
  4. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 165
  5. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Modelscited by 157
  6. 2023Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Modelscited by 133
  7. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 111
  8. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 109
  9. 2022How to Backdoor Diffusion Models?cited by 104
  10. 2022Refining Generative Process with Discriminator Guidance in Score-based Diffusion Modelscited by 100
  11. 2023Stochastic interpolants with data-dependent couplingscited by 100
  12. 2023Minimizing Trajectory Curvature of ODE-based Generative Modelscited by 89
38 more
  1. 2023Refusion: Enabling Large-Size Realistic Image Restoration with Latent-Space Diffusion Modelscited by 86
  2. 2024Variational Flow Matching for Graph Generationcited by 83
  3. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusioncited by 78
  4. 2022Multiscale Structure Guided Diffusion for Image Deblurringcited by 77
  5. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 67
  6. 2024Diffusion Models, Image Super-Resolution And Everything: A Surveycited by 64
  7. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 60
  8. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistentcited by 58
  9. 2022Efficient Diffusion Models for Vision: A Surveycited by 51
  10. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 45
  11. 2022Multiresolution Textual Inversioncited by 34
  12. 2024The Stronger the Diffusion Model, the Easier the Backdoor: Data Poisoning to Induce Copyright Breaches Without Adjusting Finetuning Pipelinecited by 33
  13. 2022f-DM: A Multi-stage Diffusion Model via Progressive Signal Transformationcited by 32
  14. 2024Self-Consistent Recursive Diffusion Bridge for Medical Image Translationcited by 26
  15. 2022Spectral Diffusion Processescited by 25
  16. 2023Graph Signal Diffusion Model for Collaborative Filteringcited by 25
  17. 2023The role of noise in denoising models for anomaly detection in medical imagescited by 23
  18. 2023Learning multi-scale local conditional probability models of imagescited by 21
  19. 2023Neural Diffusion Modelscited by 21
  20. 2024Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Modelscited by 21
  21. 2024Deep MMD Gradient Flow without adversarial trainingcited by 19
  22. 2023Learning to Jump: Thinning and Thickening Latent Counts for Generative Modelingcited by 18
  23. 2025Ambient Diffusion Omni: Training Good Models with Bad Datacited by 18
  24. 2023Beta Diffusioncited by 17
  25. 2023DiffEnc: Variational Diffusion with a Learned Encodercited by 17
  26. 2025Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusioncited by 17
  27. 2022Boomerang: Local sampling on image manifolds using diffusion modelscited by 16
  28. 2023Enhancing Diffusion Models with 3D Perspective Geometry Constraintscited by 16
  29. 2022DriftRec: Adapting diffusion models to blind JPEG restorationcited by 15
  30. 2023DiracDiffusion: Denoising and Incremental Reconstruction with Assured Data-Consistencycited by 15
  31. 2023Denoising Diffusion Semantic Segmentation with Mask Prior Modelingcited by 15
  32. 2023Removing Structured Noise with Diffusion Modelscited by 14
  33. 2023Learning Fourier-Constrained Diffusion Bridges for MRI Reconstructioncited by 14
  34. 2023Star-Shaped Denoising Diffusion Probabilistic Modelscited by 13
  35. 2023Generative Fractional Diffusion Modelscited by 12
  36. 2025Nonisotropic Gaussian Diffusion for Realistic 3D Human Motion Predictioncited by 12
  37. 2025FlexiDiT: Your Diffusion Transformer Can Easily Generate High-Quality Samples with Less Computecited by 12
  38. 2023Masked Diffusion as Self-supervised Representation Learnercited by 11

50 most cited of 102 All 102 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2024From optimal score matching to optimal sampling
  2. 2024Improving Diffusion Models's Data-Corruption Resistance using Scheduled Pseudo-Huber Loss
  3. 2024Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models
  4. 2023Reflected Diffusion Models
  5. 2021Maximum Likelihood Training of Score-Based Diffusion Models
  6. 2025Denoising Score Distillation: From Noisy Diffusion Pretraining to One-Step High-Quality Generation
  7. 2025Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves
  8. 2024Slight Corruption in Pre-training Data Makes Better Diffusion Models